Electromagnetic Induction (Flux linkage)

[JosephF]

Apologies for numerous posts today, I'm trying to catch up from work I missed last term, and my uni is on holiday at the moment so cant get help from lecturers.

I've been set the following which I think I've got correct, but not 100%. Am I right in calculating the area in m2?

1. The problem statement, all variables and given/known data

2. A rectangular coil measuring 20mm by 35mm and having 650 turns is rotating about a horizontal axis which is at right angles to a uniform magnetic field of flux density 2.5x10-3T. The plane of the coil makes an angle θ with the vertical, as shown in the diagrams.


(i) State the value of θ when the magnetic flux through the coil is a minimum.
(ii) Calculate the magnetic flux passing through the coil when θ is 30o.
(iii) What is the maximum flux linkage through the coil as it rotates?


2. Relevant equations

ΔΦ=NBAsinθ

3. The attempt at a solution

i) Φ is at a minimum when θ=0

ii) ΔΦ=650x(2.5x10-3)x(0.002x0.0035)sin30

=1.365x10-5sin30

=5.6875x10-6Wb

iii) Flux linkage is maximum when θ=90

ΔΦ=1.375x10-5sin90

=1.375x10-5Wb

Thanks,

[Cyosis]

Almost, 1 m = 1000 mm, so 20 mm =20*10^-3m=0.02m. So you're a factor 100 off regarding the area.

[JosephF]

3. The attempt at a solution

i) Φ is at a minimum when θ=0

ii) ΔΦ=650x(2.5x10-3)x(0.02x0.035)sin30

=1.1375x10-3sin30

=5.6875x10-4Wb

iii) Flux linkage is maximum when θ=90

ΔΦ=1.1375x10-3sin90

=1.1375x10-3Wb

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Ah, that was careless of me! Thanks for pointing it out. Is everything now correct. Am I right with my assumptions of min when θ=0 and max when θ=90?

Thanks,

[Cyosis]

Yes everything seems to be correct now. Your assumptions are easy to check. When theta is 0 the coil is parallel to the magnetic field so no field lines pass through the coil. When theta is 90 degrees the coil is perpendicular to the magnetic field and a maximum amount of field lines go through the coil.

[JosephF]

That brilliant. Thanks again.